We say that a function $f:M\rightarrow X$ is a of class $C^\infty$ on $M$ if it is of class $C^\infty$ on $int M$, for each multiindex $\alpha$ and for each $x$ from boundary of $M$ there exists $\lim_{y\rightarrow x \atop y\in int M} D^\alpha f(y)$, and function $D^\alpha f$ defined on $int M$ in usual sense and for $x$ from boundary by $D^\alpha f(x) =\lim_{y\rightarrow x \atop y\in int M} D^\alpha f(y)$ is continuous.